For fault diagnosis under unseen working conditions (WCs), it is crucial to extract general knowledge unrelated to data distribution from available source data and identify transferable discriminative features. However, WC-related information is often tightly coupled with health state (HS)-related information, making it difficult to directly distinguish their contributions, posing challenges to fault diagnosis. To address this issue, a novel approach named WC-decoupled and invariant-feature fusion transformer (WCD-IFFT) is proposed, which aims to minimize the impact of WCs by extracting transferable features closely related to HSs. Specifically, two key components are designed to decouple WC-related features from HS-related features: orthogonality separation and decouple loss. Additionally, to enrich the semantics of HS-related features, time-domain and Fourier phase features are mapped into a unified space and fused, combining the instantaneous changes of time-domain signals with frequency-domain distribution information to enhance the feature representation capability. Extensive experiments on cross-domain fault diagnosis tasks demonstrate the effectiveness of the proposed method.

Federated learning (FL) and zero-shot learning have been becoming increasingly popular due to the data-privacy protection and the diagnosis of unseen faults in the industrial fault diagnosis. However, most existing diagnosis methods have the consistency assumption of distributions across different clients under multisource domain scenarios and cannot effectively diagnose both seen and unseen faults. Therefore, to diagnose both seen and unseen faults without data sharing and with distribution discrepancies across different clients, a federated generalized zero-sample fault diagnosis (GZSFD) paradigm is proposed in this article. In the client side, a stacked autoencoder (AE)-based feature extractor is introduced in each client for low-level features. In the cloud server, a feature-level distribution alignment scheme is developed to alleviate discrepancies for more discriminative high-level features. Moreover, a bidirectional AE (BAE) with reconstruction and cross-reconstruction streams is designed to enhance the feature-semantic consistency. Finally, a gating model based on BAE is proposed to identify online samples and mitigates the misclassification of unseen samples. Results on two practical industrial cases show that the proposed method achieves the improvement in federated GZSFD and effectively handles distribution discrepancies across different clients.

In this paper, we construct non-binary codes of lengthNwhich correct errors under a non-binary segment-Nmaxburst-Ddeletion and maxburst-Sinsertion (NB-SBDI(N, D, S)) channel without knowing the codeword boundaries. In this NB-SBDI(N, D, S) channel, at most a single non-binary burst (a block of consecutive bits/symbols) of deletions or insertions of length up toDorS, respectively, exists in a block ofNconsecutive non-binary symbols. One code named as BM-DB-MDS consists of a maximum distance separable (MDS) code, a block of periodic de Bruijn (DB) symbols, and a block of proposed periodic binary marker (BM) patterns with a period ofS+D+ 2. The other code called BM-MDS code consists of a BM code and an MDS code. We show that the rates of BM-DB-MDS and BM-MDS codes achieve λ/λ+1 (1 - 1/2t), λ ∈ N+and 1 - 1/t, respectively, whenN→ +∞, where λ represent the MDS code shortening factor, and 1/tis the rough proportion of the maximum length of burst deletions or insertions allowed in a code.